1. Field of the Invention
The present invention relates to an articulated manipulator comprising a plurality of links, and joints rotatably connecting the links. More particularly, the present invention relates to an articulated manipulator comprising a plurality of links, and coaxial joints each for connecting the two adjacent links for coaxial rotation, and diagonal joints each for connecting the two adjacent links such that one of the two adjacent links makes a conical revolution relative to the other.
2. Description of the Related Art
Prior art related to articulated manipulators disclosed in, for example, JP62-148182A, JP56-163624A and JP2001-138279A has a diagonal joint connecting two links. The diagonal joint connects the two links such that one of the two links makes a conical revolution on the diagonal joint. Each of the two adjacent links connected by the diagonal joint revolves about a rotation axis inclined at a predetermined angle to its axis.
For example, an articulated manipulator comprises a plurality of links arranged in series, and a plurality of joints rotatably connecting the adjacent links, respectively. The joints include coaxial joints and diagonal joints. The coaxial joint connects the adjacent links so that the adjacent links are able to turn about a rotation axis aligned with their axes. The diagonal joint connects the adjacent links such that one of the two adjacent links is able to make a conical revolution relative to the other about a rotation axis inclined at an angle to its axis.
The articulated manipulator moves a terminal device connected to its terminal end along a predetermined path. The motion of the terminal device needs to be converted into the respective turning motions of the links to move the terminal device by the articulated manipulator; that is, the rotation angles of the links must be determined by inverse transformation on the basis of a position at which the terminal device is to be positioned and an orientation in which the terminal device is to be set.
According to the prior art disclosed in JP56-163624A, the inverse transformation is impossible unless the articulated manipulator has seven joints connecting the links, namely, a coaxial joint, a diagonal joint, a coaxial joint, a diagonal joint, a coaxial joint, a diagonal joint and a coaxial joint arranged in that order. In the case of using this prior art, analytical solution cannot be obtained through inverse transformation for an articulated manipulator having less than seven joints. Therefore, there has been no articulated manipulator having six or less joints.
If there is an articulated manipulator having six joints, complicated simultaneous equations must be solved for inverse transformation. It is difficult to obtain analytical solutions even if a computer capable of executing a formula manipulation program is used for solving the complicated simultaneous equations. Therefore, the rotation angles of the links of an articulated manipulator having six or less joints must be determined by a convergence operation, such as an operation using the Newton-Raphson formula. The rotation angles of the links cannot be determined quickly by the convergence operation.
Technique disclosed in JP2001-138279A determines rotation angles of the links by an interpolatory approximation method. This method determines a representative point and orientation of the terminal end of the articulated manipulator by an analytical direct transformation after the rotation angles of the links are determined, and stores rotation angles of the links with the terminal device located at a plurality of representative points in a database beforehand. Inverse transformation determines rotation angles of the links by interpolatory approximation using data included in the database. The terminal end of an articulated manipulator having less than seven joints cannot accurately be positioned and oriented by operating the articulated manipulator on the basis of this method because the rotation angles are approximate values.
FIG. 10 shows a part of an articulated manipulator 1 whose location is controlled by interpolatory approximation. Generally, the articulated manipulator 1 stores rotation angles of its links when a terminal device 10 is located at representative points. For example, to move the terminal device 10 from a first representative point A to a second representative point B, the articulated manipulator 1 reads the rotation angles of the links with the terminal device 10 at the representative point A, and those of the links with the terminal device 10 at the representative point B from the database. Then, the articulated manipulator 1 carries out interpolatory calculations using the rotation angles of the links with the terminal device 10 at the representative point A and those of the same with the terminal device 10 at the representative point B to determine interpolated rotation angles. The links are turned to the interpolated rotation angles to shift the terminal device 10 from the representative point A to the representative point B.
Since the links are turned to the rotation angles determined by interpolatory approximation, the terminal device 10 cannot accurately be located; that is, the terminal device 10 cannot smoothly moved along a prescribed path.
There are a plurality of combinations of the rotation angles of the links to set the terminal device 10 in a desired orientation at a desired position. However, when the rotation angles of the links are determined by a convergence operation or interpolatory approximation, only a single combination of rotation angles can be determined and hence an optimum combination of rotation angles of the links cannot be determined.
The rotation angles of the links of the articulated manipulator having six or less joints cannot analytically be determined in locating the terminal device 10 in a desired orientation at a desired position and, consequently, the terminal device 10 cannot quickly and accurately be located in the desired orientation at the desired position. Moreover, a plurality of combinations of the rotation angles of the links cannot be determined.